Wavefront analysis is based on the proposition that light has a characteristic wavelength, and that phase differences in wavelength between contiguous individual light beams are descriptive of the wavefront. In order to better understand this proposition, it is helpful to also understand the meanings of "wavefront" and "phase" in the context of light. By definition, wavelength is the distance between two similar and successive points on a harmonic (sinusoidal) wave, e.g. the distance between successive maxima or minima. Accordingly, in one wavelength, the waveform will go through one complete cycle from maxima to maxima, or minima to minima. Further, by definition, phase is the fraction of a cycle of a periodic waveform which has been completed at a specific reference time. Typically, the phase of a waveform is determined relative to the start of a cycle of another waveform of the same frequency. Further, phase can be expressed either as an angle, with one cycle corresponding to 2.pi. radians (or 360.degree.), or as a fraction of a wavelength (.lambda.). For example, the same phase shift can be expressed either as a 90.degree. phase shift, or as a .lambda./4 phase shift.
A wavefront of light can be thought of as a plurality of individual light beams which are all contiguous with each other. In accordance with the definitions given above, a plane wavefront of monochromatic light occurs when all of the light is in phase as it is incident on, or passes through, a plane that is oriented perpendicular to the path of the light. Thus, for a plane wavefront, the light in the wavefront can be thought of as including a plurality of contiguous individual light beams in which the light in any one light beam is in phase with the light in all of the other light beams. On the other hand, when light in one or more of these contiguous individual light beams is out of phase with the light in other light beams, i.e. there are phase deviations in the light, the result is a distorted wavefront. These phase deviations, however, can be measured and, thus, can be used to describe or define the wavefront. For example, methods for measuring phase deviations have been disclosed in conjunction with devices like the well known Hartmann-Shack sensor and in publications such as U.S. Pat. No. 5,062,702 which issued to Bille for an invention entitled "Device for Mapping Corneal Topography."
Insofar as an eye is concerned, it is known that a wavefront analysis can be used to determine the refractive properties of the eye. Also, by comparing the refractive properties of a particular eye to those of a "normal" eye, a wavefront analysis can be used to determine what corrective actions, if any, are appropriate. For these purposes, the "normal" eye is known to have a pupil that has an approximately six millimeter diameter, when dilated. Also, the "normal" eye is known to accommodate a maximum phase shift gradient of approximately one wavelength per millimeter (1.lambda./mm). Stated differently, a "normal" eye can effectively accommodate a phase change equal to one wavelength over a distance of one millimeter. For wavefront analysis, this one millimeter distance is taken in a direction that is perpendicular to the path of the contiguous individual light beams in the wavefront of light that is incident on the eye.
A widely used criteria for rating the quality of an optical system, either mechanical or anatomical, is the so-called Strehl ratio. Mathematically, the Strehl ratio, "S", can be expressed as S=I/I.sub.o, where "I" is the maximum intensity of the real system being evaluated and, "I.sub.o " is the maximum intensity of an ideal optical system (with the same aperture diameter and F/number). The Strehl ratio may be expressed either as a ratio or as a percentage. For an ideal optical system, the Strehl ratio is 1 or 100%. For a very good optical system the Strehl ratio is more than 0.9 or 90%, and for a diffraction limited system, the Strehl ratio should be greater than 0.8 or 80%. The Strehl ratio for a "normal" eye is 0.9 (S=90%) over a pupil with a diameter of approximately three millimeters (3 mm), under daylight illumination conditions.
With the above in mind, the optical capabilities of an eye can be described in terms of phase shift, phase shift gradient and the Strehl ratio. Specifically, it is known that the "normal" eye is able to accommodate an r.m.s. error in phase deviations of about .lambda./14 with a 3 mm pupil without any appreciable diminution in visual acuity. Insofar as phase shift gradient is concerned, as implied above, a gradient of 1.lambda./mm is considered "normal" beyond the 3 mm pupil and corresponds to a Strehl ratio of approximately S=0.1 over a pupil of approximately 6 mm in diameter under twilight illumination conditions. Further, it is known that the steepest gradient which can be effectively accommodated by an eye is approximately 5.lambda./mm.
Accordingly, in light of the above it is an object of the present invention to provide a method and device for programming an active mirror which will transform a distorted wavefront into a plane wavefront, and vice versa, while effectively compensating for as much as a 5.lambda./mm phase shift gradient. Another object of the present invention is to provide a method and device for programming an active mirror which will transform a distorted wavefront into a plane wavefront, and vice versa, while accounting for modular n2.pi. (or n.lambda.) phase shifts. Still another object of the present invention is to provide a method and device for programming an active mirror which is simple to use, relatively easy to manufacture and comparatively cost effective.